In this paper we mainly study the vertex operator algebra CVA(e,f) generated by two Ising vectors e and f with 〈e,f〉=5210. We prove is isomorphic to 6A-algebra U6A constructed in [20]. also discuss cases 〈e,f〉=14,125, 0 case 〈e,f〉=128 (τeτf)4=1.

In this paper, we determine the trivial factors of L-functions of both finite and infinite symmetric products of Kloosterman sheaves. Let Fq be a finite field of characteristic p with q elements, let l be a prime number distinct from p, and let ψ : Fq → Q ∗ l be a nontrivial additive character. Fix an algebraic closure F of Fq. For any integer k, let Fqk be the extension of Fq in F with degree ...

Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes in G.

In this paper we review various strikingly parallel algebraic structures behind Hilbert schemes of points on surfaces and certain finite groups called the wreath products. We explain connections among Hilbert schemes, wreath products, infinite-dimensional Lie algebras, and vertex algebras. As an application we further describe the cohomology ring structure of the Hilbert schemes. We organize th...

A brief survey of real algebraic structures on topological spaces is given.

Let X be an infinite set of cardinality κ. We show that if L is an algebraic and dually algebraic distributive lattice with at most 2 completely join irreducibles, then there exists a monoidal interval in the clone lattice on X which is isomorphic to the lattice 1 + L obtained by adding a new smallest element to L. In particular, we find that if L is any chain which is an algebraic lattice, and...

In this paper we construct several examples of partial linear spaces. First, we define two algebraic structures, namely the spaces of k-pencils and Grassmann spaces for vector spaces over an arbitrary field. Then we introduce the notion of generalized Veronese spaces following the definition presented in the paper [8] by Naumowicz and Prażmowski. For all spaces defined, we state the conditions ...

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.

1. Introduction The subject of the present paper is the search for examples of Riemann tensors which contain terms with a structure of certain generators of algebraic curvature tensors. Let V be a finite-dimensional K-vector space, where K is the field of real or complex numbers. We denote by T r V the K-vector space of covariant tensors of order r over V .

In this paper we identify the “nil-terms” for Waldhausen’s algebraic K-theory of spaces functor as the reduced Ktheory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.